4.1. Quantum Technologies
It has been considered that classical mechanics deals with macroscopic particles and quantum mechanics deals with microscopic particles. However, any concrete size to distinguish between macroscopic particles and microscopic particles has not been defined. From elementary particles to atoms or molecules, such particles that cannot possibly be observed using optical microscopes are assumed to be referred to as microscopic particles. This is merely a factitious criterion that existed around 80 years ago, when quantum mechanics was created. Nowadays, since electron microscopes etc. have been developed, the microscopic world has become almost visible except for the inside of each atom. Therefore, we must recognize afresh that the above distinction does not exist in nature itself. According to quantum mechanics, since individual microscopic particles have particular properties quite different from those of macroscopic particles, various phenomena peculiar to microscopic particles are expected to occur. Over the past dozen years or so, patents disclosing that the above properties and phenomena peculiar to microscopic particles have been applied to specific apparatus and technologies in the field of advanced information processing such as quantum computers and quantum cryptographic communications have come to be filed. The ‘principle of superposition of states’ exists as one of the fundamental principles in quantum mechanics. Those quantum computers utilize individual atoms or molecules, each of which may take a certain superposed state conforming to the above superposition principle, and individual optical or electronic devices produced by simulating the above atoms or molecules as memory and/or calculation devices dealing with each individual quantum mechanical information unit, i.e., quantum bit (qubit). Here, these devices for quantum bits are called quantum devices for convenience. The demand for fast computations is the highest in the field of cryptology using algorithms for prime factor decomposition. This is because it is necessary to protect valuable information that is exchanged through a communication network not limited to the Internet, through encryption. The currently used encryption method is said to take hundreds of years to decrypt even using a high-speed computer. If this encrypted information is wiretapped and decrypted in a short time by applying a quantum algorithm for prime factor decomposition, this encryption method cannot be used. On the other hand, quantum cryptographic communications have been intended for detecting wiretapping by utilizing each of the photons as individual carriers for signals. Even if quantum computers could be realized and if wiretapped cryptographs could be decrypted quickly, means for avoiding the wiretappings could be applied as long as the wiretappings could invariably be detected. In this sense, the quantum cryptographic communications function as insurance in preparation for the realization of quantum computers. As a part of this communication system, there is a case where characteristic phenomena in quantum mechanics called nonlocal correlation or correlation at a distance are utilized. As shown above, the technology contrived based on the peculiar phenomena in quantum mechanics may be called quantum technology for convenience.
4.2. Whether or not the Realization of Quantum Computers is Possible
The viewpoints of specialists on whether or not the realization of quantum computers is possible will be introduced based on recent documents:
In 2005, a review paper by Prof. Yamamoto of Princeton University entitled “Solid state quantum physics II—At the boundary between quantum mechanics and technology—” was published in the December issue of Nihon Buturi Gakkai-shi (the monthly journal published in Japanese by Physical Society of Japan) (Y. Yamamoto, Nihon Butsuri Gakkai-shi, 60, 928 (2005)). In this paper there are descriptions as follows: (1) Although the investigation on quantum mechanical measurement processes which are common ground between quantum mechanics and information science began in the 1980's, it had not been recognized as a serious science at that time. (2) Quantum algorithms for factorization, discrete logarithms, and information retrieval are superior to classical algorithms for the same. (3) Whether or not studies on quantum information should be developed into true technologies is uncertain at the present time (July 2005). In this way, it can be understood that whether or not quantum technology including quantum computers should be put into practical use is uncertain even in July 2005.
Another more academic viewpoint will be given below: Prof. Ozawa of Tohoku University published a paper I (M. Ozawa, Phys. Rev. Lett. 88, 050402-1 (2002)) in which he showed that, according to a novel uncertainty relation obtained by applying quantum mechanics, a lower limit depending on the magnitude of a measuring apparatus is proven to exist in the measurement error, resulting in obstruction of the realization of a small quantum computer. Furthermore, Prof. Ozawa published a paper II (M. Ozawa, Phys. Lett. A 299, 1 (2002)) in which he showed that a measurement process model breaking the Heisenberg uncertainty principle may be provided even within the framework of quantum mechanics. The paper I concluded that quantum mechanics itself denies a possibility of development of a small quantum computer, although no reference of comparison is given. Technologically, computers utilizing tubes have been tremendously developed and downsized by the emergence of semiconductor devices. Hence, if quantum computers utilizing quantum devices become larger than, for example, computers utilizing semiconductor devices, it is irrational. There are two reasons for inviting such a result that can be readily thought as irrational. One is that arguing a quantum computer in relation to the uncertainty principle but not to the principle of superposition of states is a problem. Another is that, as will be shown in 5.5.2., there have been fundamental errors in the Heisenberg uncertainty principle itself.
It has been understood that the quantum computer has not been contrived based on ‘established physical laws’. This is because, if a quantum computer should rest on ‘established physical laws’, it is impossible for realization of the computer to be uncertain even at present. Furthermore, the technology that satisfies necessary technological conditions for filing the specification of a quantum computer for a patent cannot exist yet. This is why neither patent nor application concerning the quantum computer has been cited in this invention. The Heisenberg uncertainty principle together with the ‘principle of superposition of states’ has been the most fundamental of principles. Hence, without limiting to this uncertainty principle, each individual basic physical law in quantum mechanics must be closely reexamined.
4.3. Reliability of Fundamental Principles Supporting Quantum Mechanics
In 1935, Einstein, Podolsky and Rosen (A. Einstein, P. Podolsky, and N. Rosen, Phys. Rev. A 47, 777 (1935)) showed that a paradox later called ‘EPR paradox’ taken from their initials occurred when the principle of superposition of states was applied to two-particle systems. When criteria for observables to exist were defined by using the logic directly related to the uncertainty principle, Einstein et al. showed that the uncertainty principle does not hold if the state of each two-particle system could be completely described as a wave packet by applying the principle of superposition of states to the system. In short, the criterion for a physical quantity relevant to a certain system to exist means that the value of the physical quantity can be known exactly without imposing any disturbance through measurement to the system. From this result, Einstein et al. concluded that quantum mechanics based on the Copenhagen interpretation was incomplete. Although Bohr disputed immediately, since his argument remained in the repetition of the Copenhagen interpretation in which the complementarity principle acts as a pillar, his rebuttal was not convincing (Refer to N. Bohr, Phys. Rev. 48, 696 (1935)). Incidentally, from the expression of the state of the two-particle system given in the paper by Einstein et al., existence of ‘nonlocal correlation’ or ‘correlation at a distance’ between the two free particles far apart is derived. Therefore, this correlation being utilized in a part of a quantum cryptographic communication system is sometimes called an EPR effect (C. H. Bennett, G. Brassard, and A. K. Ekert, “Quantum Cryptography”, Sci. Am. 267, 50 (1992); Japanese trans. in Nikkei Science, December 1992, pp. 50-60). On the other hand, in the same year, Schrödinger showed that, when the ‘principle of superposition of states’ on which quantum technology depends is applied to a system including a macroscopic object (cat), ‘Schrödinger's cat paradox’ occurs (E. Schrödinger, Naturwissenschaften, 23, 807 (1935)).
In recently published nonrelativistic or relativistic quantum mechanics textbooks, these quantum mechanics based on the Copenhagen interpretation have been described to be accurate theories. Strong evidence of this exists in the fact that Bell's inequality related to hidden variables that had been introduced to explain ‘nonlocal correlation’ has been negated according to the experiment on two-photon systems. However, it will be shown with this invention that the reason why Bell's inequality does not hold is not in the correctness of quantum mechanics but in the fact that the natural world does not require hidden variables. Hence, it was already pointed out in 1935 that the uncertainty principle and the ‘principle of superposition of states’ as fundamental principles in quantum mechanics had contained essential problems. Provided that what Einstein et al. and Schrödinger pointed out is correct, not only the realization of a quantum computer but also the existence of quantum mechanics itself is threatened.
In the following, the explanation of dual mechanics that is essentially built through the process of clarifying basic problems in quantum mechanics and their solutions will be given. This dual mechanics also provides a technological design method for devices and apparatus all related to microscopic particles. Hence, an explanation of those novel devices and apparatus of dual mechanical design will be given below. Since the description is long, it is divided into two for convenience. In the first half, ‘4. Background of the invention’ and ‘5. Disclosure of the invention’ will be explained. In the second half, ‘7. Best mode for carrying out the invention’ will be explained.
4.4. Physical Significance of the Experiment of Simultaneous Observation of Duality Disclosed in Patent Reference 1
An invention on methods and apparatus of simultaneously observing the wave-particle duality of each particle, e.g., each individual photon or electron has recently been patented (Patent Reference 1). This patent discloses several pieces of experimental data indicating that the simultaneous observation of duality, which is considered to be impossible using conventional technology based on the uncertainty principle, has been successful using a newly developed interferometer. These experimental data show that the simultaneous observation of wave-particle duality of each photon has been achieved, the evidence of which is explained in detail in ‘5. Disclosure of the invention (5.5.4.)’. That is, it has been proven experimentally that each individual photon is a perfect particle and a perfect wave simultaneously. The perfect wave associated with each photon means a real wave. It has been known that each photon carries its energy as a particle. Therefore, a wave that causes interference phenomenon and associates with each photon has no energy. Since this characteristic of the wave carrying no energy is common to the property of a phase wave originally conceived by de Broglie, this wave will generally be called a phase wave.
According to the law of conservation of energy including the law of conservation of number of particles, that is, the law of conservation of relativistic energy, every particle including each individual photon interferes only with itself, but two different particles never interfere with each other (Refer to P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, London, 1958), 4th ed., pp. 9-10). If we call this phenomenon as the ‘principle of interference’, it is considered that this principle has been sufficiently verified in interference experiments carried out using photons, electrons, or atoms. In recent years, even interference phenomena of fullerene molecules have been experimentally demonstrated (M. Arndt et al., Nature 401, 680 (1999): to be more accurate, the phenomena observed directly in this experiment are diffraction phenomena caused by a diffraction grating). However, as will be introduced later, there is an exemplary experiment in which interference phenomena of each individual photon emitted from two independent lasers were observed. However, since this observation has been carried out under extreme artificial conditions, it may be regarded that the ‘principle of interference’ is valid for general particles except for photons in a natural environment. Therefore, according to the aforementioned ‘principle of interference’, it turns out that not only photons but also massive particles have the same simultaneous, complete duality as observed in the above-mentioned experiment on the simultaneous observation of duality. The proposal of a matter wave, also known as a phase wave, by de Broglie for the wave associated with each massive particle comes to mind. This matter wave or phase wave is also called the de Broglie wave named after the proponent.
In 1923, de Broglie presented the concept of a matter wave or phase wave (See, for example, L. de Broglie, Nature 112, 540 (1923)). In that paper, de Broglie showed the following three principles concerning phase waves: (a) A rest particle with mass m0 is associated with a periodic phenomenon at a frequency v=m0c2/h, (b) the phase of a phase wave that uniform velocity motion (translational motion) of the massive particle generates in an inertial system (inertial frame) is the same as that of the periodic phenomenon, and (c) a phase wave does not carry energy. Since a phase velocity that is velocity of the propagation of the phase wave is given by c2/v>c with v being velocity of the particle, the phase wave cannot carry energy. In other words, the phase wave cannot be a signal. Since the oscillation at a frequency v=m0c2/h of the rest particle with mass m0 becomes the source of the phase wave, the phase wave is clearly a relativistic wave. Originally, the phase wave had been considered to exist, because this wave associated with motion of a particle is generated and propagates in an inertial system. (This will be proven in the latter half of the description of this invention.) In contrast, a probability wave expressed by a wave function in quantum mechanics is an abstract wave that is defined in a mathematical space such as a Hilbert space having no direct relation to physical space (See, for example, P. A. M. Dirac, the aforementioned book, p. 40). Incidentally, in the aforementioned de Broglie's paper, each photon is described as having an extremely small but nonzero mass. However, according to the principle of invariant light speed, this de Broglie's idea obviously contradicts special relativity.
According to de Broglie's three principles, the space-time structure of each moving particle consists of a particle carrying energy and a phase wave without energy. In other words, the particle and the phase wave constitute a single unified particle. However, when the particle is at rest, the space-time structure of each particle consists of a particle having rest energy m0c2 and a phase space that is entirely overlapped with an inertial system fixed to the particle and is oscillating at a characteristic frequency v=m0c2/h. (As will be shown later, the phase space here is a physical existence completely overlapping real space-time and is different from a phase space in quantum mechanics.) This point differs from the case of each photon that does not have a rest mass and can never be at rest in any inertial system. However, notwithstanding whether or not it has a mass, an interference phenomenon may occur with each individual particle such as a photon or an electron due to the phase wave accompanied by the particle itself. Note that from both the conservation law of energy including the conservation law of the number of particles, which originated the ‘principle of interference’, and the aforementioned de Broglie's three principles, it can be understood that interference phenomena of massive particles occur based on the conservation law of relativistic energy including the conservation law of the particle number for low-energy phenomena and that the phase wave associated with a massive particle is also a relativistic wave as with light waves. Whether it is relativistic or not, wave functions in quantum mechanics have been determined as mathematical, probability waves. It will be shown later that confusion between mathematics and physics often seen in quantum mechanics proves fatal to this mechanics after all.
As described above, the simultaneous observation experiment showed simultaneous, complete duality of individual photons and the reality of individual phase waves associated with these photons. This result can readily be generalized to the simultaneous, complete duality of individual massive particles and the reality of individual de Broglie waves associated with these particles based on both the aforementioned Dirac's principle of interference and interference experiments concerning photons and various massive particles supporting this principle. Accordingly, it can be concluded that the reason for every type of particle not limited to photons which causes each of interference phenomena is that individual particles have respective real phase waves.
This simultaneous, complete duality that every particle has is fundamentally incompatible with wave-particle complementary duality for each particle that is a part of the complementarity principle proposed by Bohr (N. Bohr, Nature, 121, 580 (1928); refer particularly to p. 586) in connection with the uncertainty principle. Since this wave-particle complementary duality in Bohr's complementarity principle including an extremely broad concept has been completely contradicted by the above-mentioned simultaneous observation experiment, the uncertainty principle on which the complementarity principle is based is strongly questioned. This is because, according to the uncertainty principle, it has been asserted to be impossible to observe both the wave and particle properties of each individual particle simultaneously (See, for example, D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, N.J., 1951), p. 118). In addition, although Feynman et al. (R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. III (Addison Wesley, Reading, 1965) p. 1-1) described that interference of each particle is the most mysterious physical phenomenon, the simultaneous, complete duality of each particle shown in the above experiment easily solves this problem. While each particle can pass through either slit of a double slit, each real phase wave accompanied by the particle can interfere with itself after passing through both of the slits. In this way, the results of the above simultaneous observation experiment show that, simultaneous to Bohr's complementarity principle, the Heisenberg uncertainty principle is also clearly an error.
4.5. Failure of the Principle of Superposition of States Caused by the Reality of Wave Functions
An extremely important issue in physics will be pointed out here. If a wave associated with a particle exists, then the state of the particle and a wave function representing the state retain a one-to-one correspondence on a real time axis. In contrast, according to the superposition principle in quantum mechanics, the state of a particle and a wave function representing the state do not have a one-to-one correspondence (Refer to D. Bohm, the above-mentioned book, p. 126). Imagine, for example, a single molecule that can have an excited state and a ground state. The two eigenstates of this two-level molecule are represented by high-energy excited state ψ1 and ground state ψ2. Evidence that the logic of a quantum computer utilizing individual molecules as quantum bits is analog is that, in general, the state of the single molecule can be represented in accordance with the principle of superposition of states byψ=a1ψ1+a2ψ2(<ψ1|ψ2>=0, |a1|2+|a2|2=1)  (1)(Refer to, for example, Nobuyuki Emoto, “Quantum computing”, KOGAKU 28, 209 (1999) (in Japanese)). However, the reason why the condition <ψ1|ψ2>=0 has been provided newly is because the above equation represents the superposition of the eigenstates. In the case of expressing the superposition in terms of interference, this condition must be altered to <ψ1|ψ2>≠0. The essential importance of the distinction between these two cases will be shown later. When observing a particle whose superposed state is represented by Eq. (1), only either the particle with energy E1 represented by the state ψ1 or the particle with energy E2 represented by the state ψ2 is observed. As such, when applying the superposition principle represented by Eq. (1) to the two eigenstates of each single free molecule, the energy of this molecule becomes indeterminate between E1 and E2. Obviously, the expression of Eq. (1) does not satisfy the conservation law of energy. This is because the conservation of energy of a single molecule means that the energy of the molecule is kept constant as long as there is no incoming or outgoing of new energy.
On the other hand, if the state of one single molecule is represented by a real wave function, this molecule takes either one of the two states: the eigenstate ψ1 for the molecule before emission of energy and the eigenstate ψ2 for the molecule after emission. Therefore, the state of the molecule and the wave function representing the state have a one-to-one correspondence on a real time axis. Accordingly, regardless of whether or not the state of the molecule is observed, the energy conservation law is automatically satisfied. Conversely, when the energy conservation law is valid, Eq. (1) becomes invalid. Thus, it is finally understood that to consider Eq. (1) as representing a single particle able to take any analog state represented by superposing ψ1 and ψ2 with the use of coefficients a1 and a2 is wrong. From a technological viewpoint, a quantum computer utilizing quantum bits, each of which may have the state represented by Eq. (1), has something in common with perpetual motion in the sense that each quantum bit contradicts the law of conservation of energy. Consequently, quantum computers cannot be apparatus making use of natural laws. Similarly, if wave functions exist, it will later be shown that “entangled states” cannot also exist. Thus, quantum computers that utilize both the superposed states and the “entangled states” for decryption would be doubly impossible to realize regardless of their sizes being large or small.
The superposed states being able to exist in the sense that the states are consistent with the energy conservation law are produced in the structure of an interferometer in which <ψ1|ψ2>≠0 is verified. However, the definitions of quantum bits and “entangled states” based on the ‘principle of interference’ must be determined case by case by ourselves in accordance with the concrete structure of the interferometer different from the case in which, for example, quantum bits are defined by Eq. (1) representing the ‘principle of superposition of states’. Therefore, when applying many quantum bits, the interferometer becomes much complex and, at the same time, the definition of “entangled states” become extremely complex and abstract. Whatever the case, when the wave function for each photon exists, the “entangled states” of photons cannot exist. Therefore, with this invention, discussions on quantum computers utilizing “entangled states” for photons will no longer be continued.
As shown above, together with the reality of individual wave functions, the energy conservation law also prohibits application of the principle of superposition of states expressed by Eq. (1) to each single particle. When the energy conservation law is valid, wave functions exist and Eq. (1) becomes invalid. Inversely, when Eq. (1) is valid, the energy conservation law and the reality of wave functions become invalid. Accordingly, it must be stressed again that, at least, as long as the energy conservation law holds, Schrödinger's cat paradox will never occur even for individual microscopic particles as well as for individual macroscopic particles. As for quantum computers contradicting both the reality of wave functions and the energy conservation law, it has clearly been suggested that the realization of them is impossible regardless of whether their sizes are large or small. The existence of basic errors in such fundamental principles supporting quantum mechanics as the uncertainty principle and the principle of superposition of states must be recognized as an unquestionable fact.
It was stated previously that the clear distinction between the superposition of states in the sense of interference where <ψ1|ψ2>≠0 holds and the superposition of eigenstates where <ψ1|ψ2>=0 holds is extremely important. This importance is easy to understand when we hear that EPR paradox and Schrödinger's cat paradox are related only to the principle of superposition of states violating the energy conservation law without any relation to the principle of interference conforming to the law of conservation of relativistic energy. In this connection, the fact that interference phenomena are relativistic effects is inferred from the description by Dirac himself. (Refer to P. A. M. Dirac, the above-mentioned book, p. 9: It is specified here that interference phenomena conform to the energy conservation law, which includes the law of conservation of the number of particles.)
Hereafter, the superposition of states in the sense of interference will be called simply ‘principle of interference’ and superposition of states in the sense of producing wave packets will be called ‘principle of superposition of states’ to make a clear distinction between these two principles. Incidentally, there have been no textbooks for quantum mechanics in which these two principles have been distinguished clearly.
4.6. The Necessity of Statistical Wave Functions
It has empirically been known that the ‘principle of superposition of states’ is effective in the case where the result of an experiment in which each of a large number of particles is involved is described statistically. Consequently, an idea to interpret the wave function not as a probability wave for each particle but a statistical wave for a large number of particles is generated. Concerning this statistical interpretation of quantum mechanics, we can refer to an ingenious review paper by Ballentine (L. E. Ballentine, Rev. Mod. Phys. 42, 358 (1970)). An advantage of this interpretation is at least that the dissolution of Schrödinger's cat paradox can be expected. However, the effectiveness of this interpretation for the EPR paradox is unclear. Above all, the problem of this statistical interpretation is that, since it is nothing more than an alteration of interpretation, any concrete change in the formalism (mathematical formulation) of quantum mechanics is not seen and that it rather recedes from solving the intrinsic problem of interference of each individual particle with itself. It has been shown that, when the reality of the wave function associated with each particle is assumed, since the energy conservation law stands, Schrödinger's cat paradox turns out to be resolved. Accordingly, apart from real wave functions, the necessity of taking statistical wave functions into consideration in order to describe the result of an experiment in which an unspecified large number of particles is concerned arises. Thus, the ‘principle of superposition of states’ has the significance of its existence as a statistical principle applicable to these statistical wave functions. As is clear from the above consideration, the largest problem in the formalism of quantum mechanics has existed entirely in neglect of the distinction between the real wave function representing the state of each individual particle and the statistical wave functions describing the result of an experiment in which a large number of particles is involved.
The uncertainty principle also has no consistency with the energy conservation law as is the principle of superposition of states. This is because, different from classical mechanics, the position and the momentum of a single particle are uncertain having no simultaneously determined values (See, for example, D. Bohm, the above-mentioned book, pp. 100-101). On the other hand, the invention of the aforementioned Patent Reference 1 has disclosed a method of experimentally demonstrating that each particle has simultaneous, complete duality upsetting the established theory that, according to the uncertainty principle, the simultaneous observation of wave-particle duality of each individual particle is impossible. The property of a perfect particle means at least that each free particle simultaneously has a certain definite position and a certain definite momentum regardless of whether the particle is microscopic or macroscopic. This shows that the considerations and conclusions due to Einstein et al. (A. Einstein, P. Podolsky, and N. Rosen, the above-mentioned paper) had been correct. This result suggests that the uncertainty principle also is essentially a statistical principle applied to an ensemble of all individual particles each of which is measured for its position and momentum. It is clear that quantum mechanics has been so far constructed based on the principle of superposition of states and the uncertainty principle, both of which are inconsistent with the energy conservation law. Previously, it has been shown that phase waves and de Broglie waves are relativistic waves. It is also clear that nonrelativistic quantum mechanics cannot be wave mechanics for relativistic waves. Consequently, as will be shown later in 7.1.1., the nonrelativistic Schrödinger equation also turns out not to be a physical equation.
4.7. The Dirac Equation Contradicting Special Relativity
Wave functions have been regarded as probability waves also in relativistic quantum mechanics. Therefore, relativistic quantum mechanics also leads to phenomena contradicting classical mechanics or, specifically, special relativity. For example, according to the Dirac equation, a free electron in motion associates with microscopic trembling motion (Zitterbewegung) with light velocity ±c (P. A. M. Dirac, the above-mentioned book, p. 262). Regarding an electron as a classical particle having rest mass m0 and velocity v, its relativistic energy can be written also as
                    E        =                                                            m                0                            ⁢                              c                2                                                                    1                -                                                      v                    2                                                        c                    2                                                                                =                                                                      m                  0                                ⁢                                  c                  2                                                                              1                  -                                      β                    2                                                                        ⁢                                                  ⁢                          (                              β                ≡                                  v                  /                  c                                            )                                                          (        2        )            (See, for example, L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, translated by H. Hamermesh (Pergamon Press, Oxford, 1962), revised 2nd ed., p. 27.) Substituting V=±c in the above equation, this energy diverges to ∞. Then, although the velocity v has been interpreted as a velocity of the center of mass that is obtained by averaging the above microscopic trembling motion, the velocity v used in a Lorentz transformation has no such meaning as an average velocity. In this way, Dirac's relativistic theory of electrons (P. A. M. Dirac, Proc. Roy. Soc. 117, 610 (1928); ibid, 118, 351 (1928)) evidently violates the definition of relativistic energy, i.e., Eq. (2). Dirac stated that, according to the uncertainty principle, each individual electron can move with velocity ±c. If the energy divergence to ∞ is allowed by the uncertainty principle, the uncertainty principle itself becomes also the principle of nonconservation of energy as previously pointed out. Thus, it is seen that the principle of nonconservation of energy has been maintained also in relativistic quantum mechanics. Therefore, although the contents of the experiment of the simultaneous observation of duality for photons (Patent Reference 1) will be explained later in detail in ‘5. Disclosure of the invention (5.5.4.)’, detailed investigation of the thought experiment of Heisenberg's microscope will be given prior to that explanation. Then, it will become clear that the uncertainty principle had been derived as a result of mistaking measurement of the position of a single bright point for the resolution of two neighboring bright points using a microscope. As a result, the quantum mechanical world described by the uncertainty principle, that is, the Copenhagen interpretation, has turned out to be the wrong image for the microscopic world. The motion of each electron with velocity ±c can never be allowed by the uncertainty principle.4.8. Systematic Representation of Conventional Mechanics
As a summary of the above, an outline of a structure of an old system of mechanics consisting of relativistic quantum mechanics, nonrelativistic quantum mechanics, and classical mechanics established before this invention is shown in FIG. 1. Quantum statistical mechanics, quantum field theory, i.e., a developed form of quantum mechanics accompanied by divergence difficulty, quantum electrodynamics, and the theory of elementary particles have been excluded from this drawing. One of the reasons of these exclusions is that the inventor is not familiar with these fields. However, there are two other reasons more essential than the above. The first reason is that the object systems to be dealt with are restricted under the following two conditions: (i) The density of particles included in the system is so low that interaction among the particles is negligible. Consequently, each individual particle behaves as a free particle when there is no external field. (ii) The conservation of energy including the conservation of the number of particles is maintained. The second reason is, as already roughly shown, that nonrelativistic quantum mechanics and relativistic quantum mechanics, that is, the basis of the above fields, can be definitely shown as non-physical theories based on the following two grounds: (1) Both mechanics contradict special relativity. (2) Both mechanics are based on the uncertainty principle that was established based on elementary errors by Heisenberg.
Referring to FIG. 1, the conventional system of mechanics will be explained simply. In the explanations below, the basis of all mechanics is largely categorized into three mechanics, that is, from the top in this drawing, relativistic quantum mechanics, nonrelativistic quantum mechanics, and classical mechanics. Classical mechanics can be regarded as consisting of Newtonian mechanics, special relativity, the general theory of relativity (general relativity), and statistical mechanics. Special relativity converts into Newtonian mechanics simultaneously when Lorentz transformations are changed over to Galileo transformations through the procedure as c→∞. There are two fundamental equations in relativistic quantum mechanics: The Klein-Gordon equation is applied to spin-0 particles and the Dirac equation is applied to spin-1/2 particles, both of which are covariant under the Lorentz transformations. Wave functions satisfying these wave equations have been regarded as probability waves, as in the case of nonrelativistic quantum mechanics, and the principle of superposition of states and the uncertainty principle are valid. But, according to Dirac, the principle of superposition of states is considered a relativistic principle (Refer to P. A. M. Dirac, the above-mentioned book, p. 253). Relativistic quantum mechanics changes over to nonrelativistic quantum mechanics through the procedure of nonrelativization, substantially resulting in m0c2=0. From this fact, it is very clear that nonrelativistic quantum mechanics violates the conservation of relativistic energy. As for fundamental equations in nonrelativistic quantum mechanics, there exist the Schrödinger equation also derived by the nonrelativization of the Klein-Gordon equation and the Pauli equation obtained by the nonrelativization of the Dirac equation. The Pauli equation, however, seldom comes to the surface. Although the Schrödinger equation has been regarded as covariant under the Galileo transformation, this problem will be discussed later again. Further, nonrelativistic quantum mechanics has been regarded as changing over to Newtonian mechanics through the procedure of h→0. Conversely, nonrelativistic quantum mechanics can be derived from analytical dynamics, that is, a developed form of Newtonian mechanics, through the procedure of quantization. In this procedure, since rest energy is ignored, it substantially gives m0c2=0. Theoretically, if m0c2=0, atomic power generation becomes impossible and, therefore, atomic power engineering cannot stand under nonrelativistic quantum mechanics. In other words, nonrelativistic quantum mechanics is clearly disqualified for the basic theory of all engineering.
The largest feature indicated by the system of mechanics depicted in FIG. 1 is the existence of the thick wall by which quantum mechanics dealing with microscopic particles conforming to nonconservation of energy and classical mechanics dealing with macroscopic particles conforming to conservation of energy are isolated from each other. 80 years have passed since the origination of quantum mechanics in 1925. However, although foundations of quantum mechanics even including Dirac's relativistic theory of electrons (P. A. M. Dirac, the above-mentioned papers of 1928, the hole theory of 1930, etc.) had been established in only 4 to 5 years, noticeable progress of quantum mechanics has not been seen since. The premise of conforming to conservation of energy must be established in any field of engineering. Quantum mechanics that has disregarded conservation of relativistic energy since its origination cannot provide theoretical foundations in recent fields of advanced and precise engineering. On the contrary, as seen in quantum computers, quantum mechanics that has been left behind by continuous progress of engineering during the past 80 years has begun to prevent normal development of advanced technology.
[Patent Reference 1] Patent No. JP3227171